On Friday, May 2, 2014 2:15:01 PM UTC-4, muec...@rz.fh-augsburg.de wrote: > On Friday, 2 May 2014 16:54:15 UTC+2, Dan Christensen wrote:
> > After over a century of intensive scrutiny, > > > > Wrong. Most mathematicians have simply accepted what their leaders said. Some have really found contradictions but they have been silenced, i.e., their papers have rarely been mentioned by the leading matheologians. >
> > > > no one has been able to demonstrate any inconsistency arising from that the Peano's Axioms for the infinite set of natural numbers. > > > > There is no inconsistency if |N is interpreted as a potentially infinite set. >
There would be nothing -- certainly no formal development of number theory as far as I can tell.
> > > But we know that every expression that can appear in eternity in the whole, possibly infinite, universe belongs to a countable set. Therefore also every expression that can appear in the mathematical discourse belongs to a countable set. >
How do "we" know this? Is it too much to ask for a formal proof?
> > > Nothing that can appear in this discourse, which *is* mathematics, can be uncountable. >
Makes no sense.
> > > Some matheologians have argued that "definition" cannot be definied, therefore we could not talk about the countable set of definable numbers.
Makes perfect sense to me.
> But they who have argued so and they who have accepted it must be fools or, if intelligent, swindlers. We do *n* need any definition of "definition".
You need some kind of workable formalism. You haven't got one, WM.